so are we to give fed number 1 if he wins wimbledon and retains number 1 this year ?
If he ends the year number one, he's got a good argument. If he just takes it for a few weeks but, say, Novak ends the year number one, I think he'll stay where he is.
Although it's hard to compare the modern era with the time in which Tilden played. Travel was so much tougher then. Tilden was pretty unanimously considered the best tennis player in the world for quite a few years, but he mostly played in America. He traveled to Wimbledon a few times, never won the French, and never even participated in the Australian Championships. I have no idea about the overall popularity of tennis in those days, but looking at the players, it was largely just four nations competing against each other - Britain, U.S., Australia, and France - whereas today we have much greater depth with respect to the number of players and nations participating in the sport. Add to that the technological advances that make the game much more demanding and physical today, and I'm not sure we should put Tilden above Federer even now.
Laver, on the other hand, played in a much more modern era and was very competitive in his mid-late 30s with guys like Connors and Borg, so I think his case is far more solid.